The search for different ways to solve a problem, and their critical assessment in order to determine the most rational ones allow one to reveal the rich possibilities of mathematics and are an important factor in the development of students’ mathematical thinking and those qualities that will be in demand in their professional activities. The purpose of the article is to explore the readiness of future mathematics teachers to solve problems using various methods or methods and to determine the possibilities of university education in developing the knowledge and skills of students that determine this readiness. Empirical data obtained during the study and presented in the work prove that the readiness of first-year students to use different strategies to solve the same problem is quite low, but increases by the fourth year of university study due to more in-depth mastery of the school mathematics course and conducting classes where future mathematics teachers are directly involved in the search for various ways and methods of solving problems.